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How do I find the half-life of radioactive isotope?

The half-life of a radioactive isotope is the time taken for half of the atoms in a given sample of the isotope to decay. Radioactivity is random and so, half-life is the average time taken for a large number of atoms.

There are two ways to find the half-life, both come from the decay equation: N = N0e^(-λt) which is an exponential relationship*.

Where N is the number of atoms of the isotope left at time t and N0 is the number of atoms when t =0. λ is known as the decay constant and is the probability that an atom will decay per unit time. If you are given the decay constant you may find the half-life T1/2 by setting N = N0/2 and rearranging to find t = T1/2. Or if you are given N and N0 you may find λ and follow the previous steps.

*Make sure you familiar with exponentials and logs before attempting this topic

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